Elements of a color group C are colored in the following way. The
elements having the same color as C.identity form a subgroup H, which
has finite index n in C. H is called the ColorSubgroup of C.
Elements of C have the same color if and only if they are in the same
right coset of H in C. A fixed list of right cosets of H in C,
called ColorCosets, therefore determines a labelling of the colors,
which runs from 1 to n. Elements of H by definition have color 1,
i.e., the coset with representative C.identity is always the first
element of ColorCosets. Right multiplication by a fixed element g of
C induces a permutation p(g) of the colors of the parent of C.
This defines a natural homomorphism of C into the permutation group of
degree n. The image of this homomorphism is called the
ColorPermGroup of C, and the homomorphism to it is called the
ColorHomomorphism of C.
GAP 3.4.4